(see VII 1.21 of [1]}).
Then the evaluation map \(\overline{W}G^{\Delta [1]} \times \Delta [1]\rightarrow \overline{W}G\) 
gives a canonical simplicial homotopy
\({\overline{W}G^{\Delta [1]} [d] [dr] & \\\overline{W}G^{\Delta [1]}\times \Delta [1] [r] & \overline{W}G \\\overline{W}G^{\Delta [1]} [u] [ur] }\) 
